Math lesson plan · 9th grade (Year 10 in England) · 45 minutes
Solve quadratics by factorising
Algebra
CCSS HSA.REI.B.4.BCCSS HSA.SSE.B.3.AEngland: GCSE Foundation AlgebraEngland: GCSE Higher Algebra
Objective and success criteria
Students will: Solve quadratics by factorising.
- I can answer questions on today's skill on my own, without help.
- I can explain each step and say why it works.
- I can check my answer and spot a mistake.
Before and after
Needs first: Factorise quadratics x² + bx + c
Leads to: Graphs of quadratics: roots, vertex, intercepts; The quadratic formula; Quadratic inequalities
Materials: Balance scales or a balance drawing, Algebra tiles, Function machine cards, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 5 min
- Quick retrieval from earlier learning (Factorise quadratics x² + bx + c). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Factorise: x² − 13x + 36 ((x + 36)(x + 1) / (x − 9)(x − 4) / (x + 9)(x + 4) / (x − 13)(x + 1)) → (x − 9)(x − 4)Prompt: Find two numbers that multiply to 36 and add to −13.
- Factorise fully: x² − 11x + 24 → (x-3)(x-8)Prompt: Two numbers: product 24, sum −11.
- Factorise: x² + 8x + 12 ((x + 6)(x + 2) / (x + 12)(x + 1) / (x + 8)(x + 1) / (x − 6)(x − 2)) → (x + 6)(x + 2)Prompt: Find two numbers that multiply to 12 and add to 8.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Solve quadratics by factorising. Read the success criteria together.
I do: model it · 10 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: Solve: x² + 7x − 18 = 0. Give both solutions, separated by a comma.
- Step 1: (x − 2)(x + 9) = 0
- Step 2: x = 2 or x = −9
- Answer: x = -9 or x = 2
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 10 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- Solve: x² + 6x − 7 = 0. Give both solutions, separated by a comma. → x = -7 or x = 1Prompt: Factorise: find two numbers that multiply to −7 and add to 6.
- Solve: x² + 3x = 0. Give both solutions, separated by a comma. → x = -3 or x = 0Prompt: Take out the common factor x.
You do: independent practice · 10 min
- Students work on the student sheet. Circulate and check the first two answers of every student early.
- Students who finish: write a question of their own for a partner, with the answer.
The 8 questions are on the student sheet below, with answers in the key.
Exit ticket · 5 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- Solve: x² + 4x = 0. Give both solutions, separated by a comma. → x = -4 or x = 0Prompt: Take out the common factor x.
- Solve: x² − 2x − 3 = 0. Give both solutions, separated by a comma. → x = -1 or x = 3Prompt: Factorise: find two numbers that multiply to −3 and add to −2.
Watch out for
- Doing an operation to one side of an equation but not the other.
- Reading 3x as 3 + x, or thinking x always stands for one particular number.
Support and stretch
Support
- Review first: Factorise quadratics x² + bx + c.
- Use concrete materials: balance scales or a balance drawing.
- Give the first step of each question, or a partly worked example to finish.
- Pair with a confident partner for the guided practice.
Stretch
- Move on to: Graphs of quadratics: roots, vertex, intercepts; The quadratic formula; Quadratic inequalities.
- Explain a common mistake in writing and how to fix it.
- Write a word problem that uses today's skill, then solve a partner's.
Homework and more practice
Free online practice with hints and printable worksheets for this skill: eurekami.com/math/grade-9.
Free lesson plan from eurekami.com/lesson-plan-builder